Abstract
We address the uniqueness problem for weak solutions for the Navier-Stokes equations using the methods of nonstandard analysis. We obtain a new description of the class of all weak solutions in dimensions 2 and 3. This yields new proofs of the classical uniqueness results and forn=3 opens a new method of exploring the possibility of nonuniqueness of solutions or of finding function spaces with both existence and uniqueness properties.
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Capiński, M., Cutland, N.J. A nonstandard approach to the uniqueness problem for the Navier-Stokes equations. Monatshefte für Mathematik 117, 51–61 (1994). https://doi.org/10.1007/BF01299311
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DOI: https://doi.org/10.1007/BF01299311